We announce the discovery of a low-mass planet orbiting the super metal-rich K0V star HD77338 as part of our on-going Calan-Hertfordshire Extrasolar Planet Search. The best fit planet solution has an orbital period of 5.7361\pm0.0015 days and with a radial velocity semi-amplitude of only 5.96\pm1.74 m/s, we find a minimum mass of 15.9+4.7-5.3 Me. The best fit eccentricity from this solution is 0.09+0.25-0.09, and we find agreement for this data set using a Bayesian analysis and a periodogram analysis. We measure a metallicity for the star of +0.35\pm0.06 dex, whereas another recent work (Trevisan et al. 2011) finds +0.47\pm0.05 dex. Thus HD77338b is one of the most metal-rich planet host stars known and the most metal-rich star hosting a sub-Neptune mass planet. We searched for a transit signature of HD77338b but none was detected. We also highlight an emerging trend where metallicity and mass seem to correlate at very low masses, a discovery that would be in agreement with the core accretion model of planet formation. The trend appears to show that for Neptune-mass planets and below, higher masses are preferred when the host star is more metal-rich. Also a lower boundary is apparent in the super metal-rich regime where there are no very low-mass planets yet discovered in comparison to the sub-solar metallicity regime. A Monte Carlo analysis shows that this, low-mass planet desert, is statistically significant with the current sample of 36 planets at around the 4.5\sigma\ level. In addition, results from Kepler strengthen the claim for this paucity of the lowest-mass planets in super metal-rich systems. Finally, this discovery adds to the growing population of low-mass planets around low-mass and metal-rich stars and shows that very low-mass planets can now be discovered with a relatively small number of data points using stable instrumentation.